Subgroups — C₄×C₇²×C₃₁⋊C₃ #32912113

Order 18228.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₃₁⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₇×C₃₁⋊C₃	C₇	1	8	yes	maximal, direct product factor
6	C₇²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₃₁⋊C₃	C₂×C₇	1	8	yes	—
8	C₄×C₇×C₃₁	C₃×C₇	1	8	yes	complemented
9	C₇×C₃₁⋊C₃	C₄×C₇	1	8	yes	direct product factor
10	C₃×C₄×C₇²	—	31	1	no	maximal, Hall
11	C₂×C₇×C₃₁	C₂×C₃×C₇	1	8	yes	—
12	C₄×C₃₁⋊C₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇²	—	31	1	no	—
14	C₇×C₃₁	C₃×C₄×C₇	1	8	yes	complemented
15	C₄×C₇²	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃₁⋊C₃	C₂×C₇²	1	1	yes	characteristic
17	C₃×C₇²	—	31	1	no	Hall
18	C₄×C₃₁	C₃×C₇²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇²	C₂×C₃₁⋊C₃	1	1	yes	characteristic
20	C₃₁⋊C₃	C₄×C₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₄×C₇	—	31	8	no	—
22	C₂×C₃₁	C₂×C₃×C₇²	1	1	yes	characteristic
23	C₇²	C₄×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₇	—	31	8	no	—
25	C₃₁	C₃×C₄×C₇²	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₇	C₇×C₃₁⋊C₃	1	8	yes	direct product factor
27	C₃×C₇	—	31	8	no	—
28	C₂×C₇	C₂×C₇×C₃₁⋊C₃	1	8	yes	—
29	C₃×C₄	—	31	1	no	Hall
30	C₇	C₄×C₇×C₃₁⋊C₃	1	8	yes	direct product factor
31	C₂×C₃	—	31	1	no	—
32	C₄	C₇²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	31	1	no	Sylow
34	C₂	C₂×C₇²×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇²	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃×C₄×C₇²
Frattini	C₂	C₂×C₇²×C₃₁⋊C₃
Fitting	C₄×C₇²×C₃₁	C₃
socle	C₂×C₇²×C₃₁	C₂×C₃
prime radical	C₂×C₇²×C₃₁⋊C₃	C₂
cosocle	C₂×C₃₁	C₂×C₃×C₇²
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₄×C₇²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄×C₇²×C₃₁	C₃	semidirect
3. C₇²×C₃₁⋊C₃	C₄	direct (N × H)
5. C₄×C₇×C₃₁⋊C₃	C₇	direct (N × H)
6. C₇²×C₃₁	C₃×C₄	semidirect
8. C₄×C₇×C₃₁	C₃×C₇	semidirect
9. C₇×C₃₁⋊C₃	C₄×C₇	direct (N × H)
12. C₄×C₃₁⋊C₃	C₇²	direct (N × H)
14. C₇×C₃₁	C₃×C₄×C₇	semidirect
15. C₄×C₇²	C₃₁⋊C₃	direct (N × H)
18. C₄×C₃₁	C₃×C₇²	semidirect
20. C₃₁⋊C₃	C₄×C₇²	direct (N × H)
23. C₇²	C₄×C₃₁⋊C₃	direct (N × H)
25. C₃₁	C₃×C₄×C₇²	semidirect
26. C₄×C₇	C₇×C₃₁⋊C₃	direct (N × H)
30. C₇	C₄×C₇×C₃₁⋊C₃	direct (N × H)
32. C₄	C₇²×C₃₁⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇²×C₃₁⋊C₃	2
C₄×C₇²×C₃₁	3
C₄×C₇×C₃₁⋊C₃	7
C₃×C₄×C₇²	31

Subgroups — C4×C72×C31⋊C3 #32912113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇²×C₃₁⋊C₃ #32912113